Abstract : This article examines the case of an observational and demonstrational armillary sphere confused, one for the other, by fifth-century historians of astronomy He Chengtian and Shen Yue. Seventh-century historian Li Chunfeng dismisses them as ignorant, supplying the reader with additional evidence. Using their respective histories and what few written sources for the history of early imperial armillary instruments survive independent thereof, this article tries to explain the mix-up by exploring the ambiguities of ‘observation’ (guan) as it was mediated through terminology, text, materiality and mathematics. Reconstructing the material features of the ‘sight’ (yi) and ‘effigy’ (xiang), the article will reflect upon the mathematics necessary for their operation. The ‘effigy’, as Li Chunfeng defines it, is a substitute for observation; the ‘sight’, however, is so mediated by the material and mathematical sphere as to confound Li’s suggested distinction of looking through vs. looking at. In the end, the difference hardly matters, as the observational armillary spheres documented by our sources appear to have played very little role in the history of astronomy in first-millennium China, leaving us to wonder what instrument(s) were used for observation.